The Gunners have made preliminary enquiries for Benzema after identifying him as the type of “exceptional player” that Wenger has said he is looking for.

The France international’s agent Karim Djaziri ruled out a move on Thursday, telling Sky Sports that his client “will be a Real Madrid player by the end of this transfer window, 1,000 per cent”.

But Football Insider has learned that Wenger has not given up hope of enticing his countryman from the Bernabeu.

It is understood that recent conversations have taken place between the Arsenal manager and Benzema’s camp, with Wenger given encouragement that a deal could be possible.

It would not take place until later in the transfer window but Wenger is a big admirer of Benzema and would be interested in making a club-record bid if he learned that there would be a possibility of signing him. For now, Wenger is prepared to play a waiting game and see if the front man becomes available, which is unlikely to be before mid to late August.

Real’s stance is that they are only prepared to listen to offers for the 27-year-old this summer if they first manage to secure a replacement.

Wenger wants to make a significant forward signing this summer only if it is a player he regards as world-class and who would immediately strengthen his first team.

It is the same rationale Wenger had when he sanctioned the £40million signing of Mesut Ozil from Real in 2013, and the £32million capture of Alexis Sanchez 12 months ago.

Benzema has scored 134 goals in 281 matches for Real since joining the club from Lyon in 2009. He has been a regular starter since Gonzalo Higuain joined Napoli two years ago, forming a productive alliance as the central player in a front three with Cristiano Ronaldo and Gareth Bale.